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Generalized Wigner-von Neumann Entropy and Its Typicality


Speaker:Prof. Biao Wu
Affiliation:Peking University
Date:April 30, 2019 (Tuesday)
Time:4:00 p.m.
Venue:Room 522, 5/F, Chong Yuet Ming Physics Building, HKU

Abstract


We propose a generalization of the quantum entropy introduced by Wigner and von Neumann [Zeitschrift fu ̈r Physik 57, 30 (1929)]. Our generalization is applicable to both quantum pure states and mixed states. When the dimension N of the Hilbert space is large, this generalized Wigner-von Neumann (GWvN) entropy becomes independent of choices of basis and is asymptotically equal to ln N in the sense of typicality. The dynamic evolution of our entropy is also typical, reminiscent of quantum H theorem proved by von Neumann. For a composite system, the GWvN entropy is typically additive; for the microcanonical ensemble, it is equivalent to the Boltzmann entropy; for a system entangled with environment, it is consistent with the familiar von Neumann entropy, which is zero for pure states. In addition, the GWvN entropy can be used to derive the Gibbs ensemble.

Reference: Hu, Wang and Wu, arXiv: 1812.10020

Coffee and tea will be served 20 minutes prior to the seminar.

Anyone interested is welcome to attend.